(1) Field of Invention
This invention relates generally to borehole seismic surveys and particularly to vertical seismic profiles (VSPs) and related VSP data processing techniques.
(2) Background Art
It is common to perform a seismic survey to obtain information concerning subsurface geological conditions. In addition to surface seismic surveys, borehole seismic data can be acquired by generating a seismic wave by a source on the surface and sensing the seismic wave using seismic detectors placed in a borehole. The seismic detectors are operable to detect the propagating seismic wave as it passes through different areas in the subterranean strata. Inferences can be made concerning the subterrain earth formations by analyzing the seismic detector data. A vertical seismic profile (VSP) or well-to-well profile can be generated from the seismic wave information sensed by the detectors.
The seismic detectors utilized for VSP are typically 3 component (3C) geophones which are placed in firm contact with the wall of the borehole and which are operable to produce electrical signals indicative of the seismic wave or movement of the sub-terrain formations along each of the orthogonal axis of the geophone. The seismic waveforms obtained during VSP measurements typically have a compressional (P) wave component and a shear (S) wave component. This is an important aspect of VSP because fluids can only support P waves in which the particle motion comprising the wave is parallel to the direction of wave propagation, whereas solids can also sustain S waves in which the direction of particle motion is transverse to the direction of wave propagation. In analyzing the seismic wave it is sometimes important to separate or decompose the wave into its separate P and S components. Independent examination of P and S wave characteristics may be useful for analyzing the VSP data.
There are various separation or decomposition methods utilized to separate the seismic waveform into its P and S wave components. Two dimensional transform techniques have been utilized for wavefield decomposition which implicitly model the input data as the sum of a large number of plane waves. The separation of wavefields is then accomplished by operating on the transformed data and inverse transforming. However, for a reliable transform of the spatial variable to be achieved, a relatively long geophone array is required, over which medium parameters should be nearly constant. With this transform technique, if moveout changes rapidly, the separated wavefield will show smearing and a subsequent loss of spatial (vertical) resolution.
In addition to the transform technique, parametric wavefield decomposition methods have been utilized where seismic propagation through the formation is described in terms of a model incorporating a plane compressional wave and a plane shear wave propagating with unspecified velocity and direction. Values are then derived for the velocity and direction of propagation of these plane waves that provide a best fit of the model to the measurement. This method is effective if a model wherein the data is assumed to be the sum of a known and small number of locally planar wavefronts is sufficient. Such a parametric inverse method to model the downgoing P and S wavefield is described in U.S. Pat. No. 4,809,239, to Esmersoy, incorporated herein by reference. This method analyzes seismic propagation in terms of the behavior of plane wave components over a short section of a borehole. However, this method of analysis has some basic assumptions such as the measurements can be appropriately described in terms of propagation of plane wavefronts of seismic energy. Also, it is assumed that the formation is locally homogeneous and that there is no coupling between orthogonally polarized shear wave components.
The parametric inversion method described in U.S. Pat. No. 4,809,239, which models the downgoing P and S wave fields from multicomponent VSP data, has further been generalized to model wave fields on single component and upgoing data in a paper by Leaney and Esmersoy in Expanded Abstracts, 59th Annual International Society of Exploration Geophysicists (SEG) Meeting, 1989. Generalizations in formulation and solution were used in that paper. To summarize the parametric wavefield decomposition (PWD) technique, the problem of decomposing a seismic data set into its constituent wave fields is formulated as a parametric inversion, where each wave field is modeled by its Fourier components and by frequency independent parameters. Modeling the data as a sum of a small number of plane wave fields rather than a large number of plane wave fields has the advantage that a small spatial aperture is required for inversion. Also, the use of multicomponent data allows P and S wave polarization information to be included in the model. A non-linear optimization is used to estimate apparent velocities of interfering events such that no picking is necessary to obtain optimum wave field separation. Also, the method utilizes a vectorial formulation for multicomponent data which permits arrival angle and velocity estimation. The generalized method leads to a single component and two-component wave field decomposition. Computational details of the more generalized method were described in a paper by Leaney, published in Expanded Abstracts, 60th Annual International SEG Meeting, 1990.
However, a limitation with the prior art methods is the assumption of a small number of plane waves and a small spatial aperture. These assumptions, while useful in many circumstances, have limited effectiveness with complicated wavefields or arbitrary well geometries. A wavefield separation technique is needed that does not make these limiting assumptions.
The invention is a method and apparatus for anisotropic wavefield decomposition for three-dimensional (3D) Vertical Seismic Profile (VSP) data. The present method makes use of general anisotropic medium properties such as tilted TI (transverse isotropic) medium properties at the downhole receivers, common shot 3C data oriented to North, East, and Vertical geographical coordinates and handles arbitrary 3D source and receiver geometries. Having specified a range of propagation angles, slowness and polarization vectors are computed for each plane wave and a linear system is solved at each frequency to yield the scalar plane-wave amplitudes. A novel regularization scheme is used that obviates the need for eigen analysis of the steering matrix. Sums within the subsets of these scalar plane waves are constructed to provide up and down qP (P), qS (Sv), and Sh wavefields. Vector residuals can be computed for parameter testing, quality control and imaging purposes. If there are more receivers than plane waves, residuals can be minimized iteratively to determine medium TI parameters. The present wavefield separation invention is well suited to the longer array tools now available and provides superior wave type separation. This invention simplifies the job of 3C elastic wavefield separation, particularly for deviated wells and 3D geometries, thus reducing processing turn around time.
The method comprises the steps of specifying propagation angles for each wave type by specifying the angular aperture (elevation angle) and number of plane waves; accessing common shot 3C vector data for each receiver in the array; extracting medium properties local to the receiver array such as the TI elastic moduli; computing the 3D slowness and polarization vector operators at each receiver; Fourier transforming (FT) all waveforms; inverting the projection moveout matrix; applying the operator to the data at each frequency; constructing sums of subsets of plane waves based on wave type and propagation angle; and inverse Fourier transforming all waveforms.
The present invention assumes the wavefield data are made up of a broad plane wave spectrum and hence, the present invention works better for longer receiver arrays. Another advantage of the present invention is that it is fully 3D in that arbitrary well geometries are handled and 3C because all components, once oriented to a geographical (East, North, and Vertical) coordinate system, can be used in the decomposition. The more traditional 2D and 2C geometries are also handled. Also 4C seismic data (3C plus hydrophone) may be handled. The present invention uses known medium properties and plane wave propagation angles to compute the slowness and polarization vectors through a forward modeling step. These are then used to decompose the vector recording into its scalar plane wave constituents.
The present invention performs VSP elastic wavefield decomposition. It can be implemented as a software module in a VSP processing routine. It can be used in a VSP processing chain, after data rotation of 3C downhole array data to geographic coordinates, and before deconvolution and imaging. Some of the advantages and features are: many more than four (4) plane waves are determined, making it ideal for longer array tools; it uses 3D (or 2D) slowness and polarization vectors in absolute geographical coordinates, and not in a well coordinate system; slowness and polarizations are computed given medium properties and propagation angles rather than determined from the data; it handles tilted TI medium explicitly; a general 3D geometry is handled; and hydrophone data is easily included in the formulation.
These and other advantageous features of the present invention will be in part apparent and in part pointed out herein below.